The Romanian world number one did have a match point but never got to grips with the 32-year-old Hsieh on a baking Court One and lost the last five games as her opponent clawed her way back from 2-5 down in the decider.

Defeat for the French Open champion means only one of the top 10 seeds in the women’s singles have reached the last 16 — Czech seventh seed Karolina Pliskova.

She is the first women’s top seed to lose to an unseeded player at Wimbledon since Ana Ivanovic lost to China’s Zheng Jie 10 years ago, also just after winning the French Open.

Hsieh thoroughly deserved her win which booked her a fourth-round clash with Slovakia’s Dominika Cibulkova.

“This is the first time I have beaten the world number one, it is amazing,” the world number 48, who made her Wimbledon debut in 2006, said.

“I had to run and fight for every point. I tried to concentrate on my game and calm down a bit, that helped a lot. This year I have tried to enjoy more, not just tennis but life, food, strawberries and cream, lobster.

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In a sport often dominated by relentless baseline bashers Hsieh brought so much more to the party.

Cunning drop shots, often played with two hands on the racket, delicate slices and laser-like flat groundstrokes that hugged the turf kept Halep continually off balance.

She also used the volleying skills that helped her win the Wimbledon doubles title in 2013 to great effect.

Halep did not play a bad match but simply ran out of ideas at the end of an absorbing two-hour-20-minute duel full of spellbinding rallies and shots not found in coaching manuals.

“I know she’s mixing the rhythm, she’s playing everything,” Halep, 26, said. “It was really hard on grass court to do better. “She deserved to win. She had more things to do on court today. I am too tired. I was too tired. I have pain everywhere.”

A curious match began untidily with five successive breaks of serve before Halep steadied to hold for a 4-2 lead and went on to clinch the opening set.

Hsieh continued posing puzzles though and broke in the third game of the second set as she absorbed a fierce baseline barrage before punishing a clumsy Halep volley by spearing a backhand down the line to roars from the crowd.

Halep broke back with a pummelling forehand for 3-3 but dropped serve again at 4-4 when she netted at the end of a baseline duel and Hsieh then calmly held serve to take the contest into a decider.

When Halep led 4-1 and 5-2 in the final set it looked as though she would live to fight another day but Hsieh broke back and repeated the trick at 5-5 when she landed a sweetly-timed backhand into the corner and Halep could only net.

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Hsieh’s serve is hardly a weapon — her second serves often crawling over the net — but she battled back from 15-40 to deuce in the final game, then closed it out as a weary-looking Halep dumped consecutive forehands into the net.

It was only the third time Hsieh had beaten a player ranked in the top 10 although she tamed Spain’s Garbine Muguruza at this year’s Australian Open where she also enjoyed a memorable run to the last 16.